$D_{a}$-Homothetic Deformation and Ricci Solitons in $(k, \mu)-$ Contact Metric Manifolds

Abstract

In this paper, we study $(k,\mu)$-contact metric manifold under $D_a$-homothetic deformation. It is proved that a $D_3$-homothetic deformed locally symmetric $(1, -4)$-contact metric manifold is a Sasakian manifold and the Ricci soliton is shrinking. Further, $\xi^*$-projectively flat and $h$-projectively semisymmetric $(k, \mu)$-contact metric manifolds under $D_a$-homothetic deformation are studied and obtained interesting results.